Freya: An educational MATLAB GUI-based tool for generalized Fourier series

Detalhes bibliográficos
Autor(a) principal: Macedo, Humberto Gimenes
Data de Publicação: 2023
Outros Autores: Oliveira, Virginia Klausner de, Gomes, Anna Karina Fontes, Fernandes, Francisco Carlos Rocha
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Research, Society and Development
Texto Completo: https://rsdjournal.org/index.php/rsd/article/view/40312
Resumo: The Fourier analysis is a very powerful mathematical tool to decompose functions into their frequency components. Due to this, it has applications in a wide variety of fields inside the realm of science and engineering. As usual, this theory starts with a discussion about the trigonometric Fourier series, the expansion of a function in terms of sines and cosines, and then is generalized in the sense that other functions rather than the trigonometric ones can be used as an orthogonal basis, as the eigenfunctions of some specific Sturm-Liouville problems, such as Bessel functions and Legendre polynomials. In this direction, we present the so- called Freya, an educational graphical user interface (GUI) for the generalized Fourier series developed using the interactive MATLAB (MATrix Laboratory) App Designer environment. We aim to provide a user-friendly tool as a learning aid system for students to gain a comprehensive understanding of the subject as well as for teaching.
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spelling Freya: An educational MATLAB GUI-based tool for generalized Fourier seriesFreya: Una herramienta educativa en el Entorno GUIDE de MATLAB para series de Fourier generalizadasFreya: Uma ferramenta educacional em Ambiente GUIDE do MATLAB para séries de Fourier generalizadasSérie de Fourier generalizadaProblemas de Sturm-LiouvilleFunções de BesselPolinômios de LegendreMATLAB.Series de Fourier generalizadasProblemas de Sturm-LiouvilleFunciones de BesselPolinomios de LegendreMATLAB.Generalized Fourier seriesSturm-Liouville problemsBessel functionsLegendre polynomialsMATLAB.The Fourier analysis is a very powerful mathematical tool to decompose functions into their frequency components. Due to this, it has applications in a wide variety of fields inside the realm of science and engineering. As usual, this theory starts with a discussion about the trigonometric Fourier series, the expansion of a function in terms of sines and cosines, and then is generalized in the sense that other functions rather than the trigonometric ones can be used as an orthogonal basis, as the eigenfunctions of some specific Sturm-Liouville problems, such as Bessel functions and Legendre polynomials. In this direction, we present the so- called Freya, an educational graphical user interface (GUI) for the generalized Fourier series developed using the interactive MATLAB (MATrix Laboratory) App Designer environment. We aim to provide a user-friendly tool as a learning aid system for students to gain a comprehensive understanding of the subject as well as for teaching.El análisis de Fourier es una herramienta matemática muy poderosa para descomponer funciones en sus componentes de frecuencia. Por esta razón, la herramienta se puede aplicar en una amplia variedad de áreas dentro del dominio de la ciencia y la ingeniería. Como de costumbre, esta teoría comienza con una discusión de la serie trigonométrica de Fourier, la expansión de una función en términos de senos y cosenos, y luego se generaliza en el sentido de que funciones distintas a las trigonométricas se pueden usar como base ortogonal, como por ejemplo: funciones propias de algunos problemas específicos de Sturm-Liouville, como las funciones de Bessel y los polinomios de Legendre. En este sentido, presentamos "Freya", una interfaz gráfica de usuario (GUI) educativa para la serie de Fourier generalizada desarrollada utilizando el entorno interactivo MATLAB (MATrix LABoratory) App Designer. Nuestro objetivo es proporcionar una herramienta fácil de usar como un sistema de ayuda al aprendizaje para que los estudiantes obtengan una comprensión integral de la materia, así como para la enseñanza.A análise de Fourier é uma ferramenta matemática muito poderosa para decompor funções em seus componentes de frequência. Devido a isso, tem aplicações em uma variedade ampla de áreas dentro do domínio da ciência e da engenharia. Como de costume, essa teoria começa com uma discussão sobre a série trigonométrica de Fourier, a expansão de uma função em termos de senos e cossenos, e depois é generalizada no sentido de que outras funções, além das trigonométricas, podem ser usadas como base ortogonal, como autofunções de alguns problemas específicos de Sturm-Liouville, como funções de Bessel e polinômios de Legendre. Nesse sentido, apresenta-se a chamada Freya, uma interface gráfica do usuário (GUI) educacional para a série de Fourier generalizada desenvolvida usando o ambiente interativo MATLAB (MATrix LABoratory) App Designer. Nosso objetivo é fornecer uma ferramenta amigável como um sistema de auxílio ao aprendizado para que os alunos obtenham uma compreensão abrangente do assunto, bem como para o ensino.Research, Society and Development2023-02-13info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionapplication/pdfhttps://rsdjournal.org/index.php/rsd/article/view/4031210.33448/rsd-v12i2.40312Research, Society and Development; Vol. 12 No. 2; e28712240312Research, Society and Development; Vol. 12 Núm. 2; e28712240312Research, Society and Development; v. 12 n. 2; e287122403122525-3409reponame:Research, Society and Developmentinstname:Universidade Federal de Itajubá (UNIFEI)instacron:UNIFEIenghttps://rsdjournal.org/index.php/rsd/article/view/40312/32967Copyright (c) 2023 Humberto Gimenes Macedo; Virginia Klausner de Oliveira; Anna Karina Fontes Gomes; Francisco Carlos Rocha Fernandeshttps://creativecommons.org/licenses/by/4.0info:eu-repo/semantics/openAccessMacedo, Humberto Gimenes Oliveira, Virginia Klausner de Gomes, Anna Karina Fontes Fernandes, Francisco Carlos Rocha 2023-02-14T20:07:52Zoai:ojs.pkp.sfu.ca:article/40312Revistahttps://rsdjournal.org/index.php/rsd/indexPUBhttps://rsdjournal.org/index.php/rsd/oairsd.articles@gmail.com2525-34092525-3409opendoar:2023-02-14T20:07:52Research, Society and Development - Universidade Federal de Itajubá (UNIFEI)false
dc.title.none.fl_str_mv Freya: An educational MATLAB GUI-based tool for generalized Fourier series
Freya: Una herramienta educativa en el Entorno GUIDE de MATLAB para series de Fourier generalizadas
Freya: Uma ferramenta educacional em Ambiente GUIDE do MATLAB para séries de Fourier generalizadas
title Freya: An educational MATLAB GUI-based tool for generalized Fourier series
spellingShingle Freya: An educational MATLAB GUI-based tool for generalized Fourier series
Macedo, Humberto Gimenes
Série de Fourier generalizada
Problemas de Sturm-Liouville
Funções de Bessel
Polinômios de Legendre
MATLAB.
Series de Fourier generalizadas
Problemas de Sturm-Liouville
Funciones de Bessel
Polinomios de Legendre
MATLAB.
Generalized Fourier series
Sturm-Liouville problems
Bessel functions
Legendre polynomials
MATLAB.
title_short Freya: An educational MATLAB GUI-based tool for generalized Fourier series
title_full Freya: An educational MATLAB GUI-based tool for generalized Fourier series
title_fullStr Freya: An educational MATLAB GUI-based tool for generalized Fourier series
title_full_unstemmed Freya: An educational MATLAB GUI-based tool for generalized Fourier series
title_sort Freya: An educational MATLAB GUI-based tool for generalized Fourier series
author Macedo, Humberto Gimenes
author_facet Macedo, Humberto Gimenes
Oliveira, Virginia Klausner de
Gomes, Anna Karina Fontes
Fernandes, Francisco Carlos Rocha
author_role author
author2 Oliveira, Virginia Klausner de
Gomes, Anna Karina Fontes
Fernandes, Francisco Carlos Rocha
author2_role author
author
author
dc.contributor.author.fl_str_mv Macedo, Humberto Gimenes
Oliveira, Virginia Klausner de
Gomes, Anna Karina Fontes
Fernandes, Francisco Carlos Rocha
dc.subject.por.fl_str_mv Série de Fourier generalizada
Problemas de Sturm-Liouville
Funções de Bessel
Polinômios de Legendre
MATLAB.
Series de Fourier generalizadas
Problemas de Sturm-Liouville
Funciones de Bessel
Polinomios de Legendre
MATLAB.
Generalized Fourier series
Sturm-Liouville problems
Bessel functions
Legendre polynomials
MATLAB.
topic Série de Fourier generalizada
Problemas de Sturm-Liouville
Funções de Bessel
Polinômios de Legendre
MATLAB.
Series de Fourier generalizadas
Problemas de Sturm-Liouville
Funciones de Bessel
Polinomios de Legendre
MATLAB.
Generalized Fourier series
Sturm-Liouville problems
Bessel functions
Legendre polynomials
MATLAB.
description The Fourier analysis is a very powerful mathematical tool to decompose functions into their frequency components. Due to this, it has applications in a wide variety of fields inside the realm of science and engineering. As usual, this theory starts with a discussion about the trigonometric Fourier series, the expansion of a function in terms of sines and cosines, and then is generalized in the sense that other functions rather than the trigonometric ones can be used as an orthogonal basis, as the eigenfunctions of some specific Sturm-Liouville problems, such as Bessel functions and Legendre polynomials. In this direction, we present the so- called Freya, an educational graphical user interface (GUI) for the generalized Fourier series developed using the interactive MATLAB (MATrix Laboratory) App Designer environment. We aim to provide a user-friendly tool as a learning aid system for students to gain a comprehensive understanding of the subject as well as for teaching.
publishDate 2023
dc.date.none.fl_str_mv 2023-02-13
dc.type.driver.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
format article
status_str publishedVersion
dc.identifier.uri.fl_str_mv https://rsdjournal.org/index.php/rsd/article/view/40312
10.33448/rsd-v12i2.40312
url https://rsdjournal.org/index.php/rsd/article/view/40312
identifier_str_mv 10.33448/rsd-v12i2.40312
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv https://rsdjournal.org/index.php/rsd/article/view/40312/32967
dc.rights.driver.fl_str_mv https://creativecommons.org/licenses/by/4.0
info:eu-repo/semantics/openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by/4.0
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv Research, Society and Development
publisher.none.fl_str_mv Research, Society and Development
dc.source.none.fl_str_mv Research, Society and Development; Vol. 12 No. 2; e28712240312
Research, Society and Development; Vol. 12 Núm. 2; e28712240312
Research, Society and Development; v. 12 n. 2; e28712240312
2525-3409
reponame:Research, Society and Development
instname:Universidade Federal de Itajubá (UNIFEI)
instacron:UNIFEI
instname_str Universidade Federal de Itajubá (UNIFEI)
instacron_str UNIFEI
institution UNIFEI
reponame_str Research, Society and Development
collection Research, Society and Development
repository.name.fl_str_mv Research, Society and Development - Universidade Federal de Itajubá (UNIFEI)
repository.mail.fl_str_mv rsd.articles@gmail.com
_version_ 1797052618865901568

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